Theorems · Theorem · global analysis

MDifferentiableWithinAt.mvfderivWithin

∀ {𝕜 : Type u_1} [inst : NontriviallyNormedField 𝕜] {E : Type u_2} [inst_1 : NormedAddCommGroup E]
  [inst_2 : NormedSpace 𝕜 E] {H : Type u_3} [inst_3 : TopologicalSpace H] {I : ModelWithCorners 𝕜 E H} {M : Type u_4}
  [inst_4 : TopologicalSpace M] [inst_5 : ChartedSpace H M] {E' : Type u_5} [inst_6 : NormedAddCommGroup E']
  [inst_7 : NormedSpace 𝕜 E'] {s : Set M} {x : M} {f : M → E'},
  MDiffAt[s] f x →
    d[s] f x =
      fderivWithin 𝕜 (writtenInExtChartAt I (modelWithCornersSelf 𝕜 E') x f)
        (↑(extChartAt I x).symm ⁻¹' s ∩ Set.range ↑I) (↑(extChartAt I x) x)

Defined in

Mathlib.Geometry.Manifold.MFDeriv.NormedSpace

Cited by

0 results in Mathlib

Foundations

Depth 168 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

NontriviallyNormedFieldNormedAddCommGroupNormedSpaceTopologicalSpaceTopologicalSpaceChartedSpaceNormedAddCommGroupNormedSpace